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arXiv · 2504.11841

Permutation dimensions of prime cyclic groups

Jack Walsh
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Abstract

Based on recent successes concerning permutation resolutions of representations by Balmer and Gallauer we define a new invariant of finite groups: the p-permutation dimension. We define this analogously to the global dimension of a ring by replacing projective resolutions of ring modules with resolutions by p-permutation modules of modules over the group ring. We compute this invariant for cyclic groups of prime order.

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Jack Walsh. 2025-04-16. Permutation dimensions of prime cyclic groups. https://arxiv.org/abs/2504.11841

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